|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/30 05:52:40
![|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|](/uploads/image/z/3690197-53-7.jpg?t=%7C1-1%2F2%7C%2B%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B.%2B%7C1%2F1000-1%2F999%7C)
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|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
1-1/2=1-1/2
|1/3-1/2|=1/2-1/3
...
|1/1000-1/999|=1/999-1/1000
所以原式
=1-1/2+1/2-1/3+.+1/999-1/1000=1-1/1000=999/1000